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Topological strings on elliptic fibrations. (English) Zbl 1316.81075
Authors’ summary: We study topological string theory on elliptically fibered Calabi-Yau manifolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the special geometry of the deformation spaces. The polynomials are fixed by the holomorphic anomaly equations supplemented by the expected behavior at special loci in moduli space. We further expand the amplitudes in the base moduli of the elliptic fibration and find that the fiber moduli dependence is captured by a finer polynomial structure in terms of the modular forms of the modular group of the elliptic curve. We further find a recursive equation which captures this finer structure and which can be related to the anomaly equations for correlation functions.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D06 Fibrations, degenerations in algebraic geometry
14J33 Mirror symmetry (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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